Don't have much experience, but some...
I'd say you could fish...
-Saranac Lake - Very good for bass and pike. Your striper flies on a 6-7wt would do the trick.
-Lake Placid - Might have gotten too warm for this, but you can definitely get decent rainbows/browns/lakers on streamers and nymphs from the lake. More of a springtime thing, I think, but if you ask around they might still be up in the water column with the late spring and all.
-AuSable River - Fish the Catch and Release "Trophy section". It can get crowded, but it's very nice water with some nice fish.
-Adirondack ponds - This would be a nicer experience. Find a brookie pond and hike to it. Look at guidebooks or ask at a shop for which one to go to - some are stocked, some have no fish, and some have wild, native brookies.
-Or take an hour and drive to Lake Champlain to fish for Smallmouths - 3-4 pounders galore.

Dewey gave you good advice. Maybe I can expand - yeah, Lake Placid is a spring fishery (actually ice-out to 3 weeks after was my favorite time).

The Ausable is a beautiful mountain stream, and decent fishing. Check the local fly shops for patterns.

The lakes mentioned are ALWAYS good fisheries - just check local tackle shops for up-to-date info.

Brookie ponds are really traditional - the problem is finding suitable water to wade (beware of muck!) so you can cast! (You need to be able to execute a back-cast.) A lot of guys hide canoes back in so they can fish 'em properly.

NOTE: June is Black Fly month - make sure you wear GOOD repellent - the season does extend into July! The bites are BAD, even though you can hardly see the damn things!